5.2.4 Circles, PT3 Focus Practice


Question 10:
Diagram below shows two quadrants, AOC and EOD with centre O.


Sector AOB and sector BOC have the same area.
Calculate the area, in cm2, of the coloured region.
( Use π= 22 7 )

Solution:
Area of the sector AOB=Area of the sector BOC Therefore, AOB=BOC = 90 o ÷2 = 45 o Area of the coloured region = 45 o 360 o × 22 7 × 16 2 =100 4 7  cm 2


Question 11:
The Town Council plans to build an equilateral triangle platform in the middle of a roundabout. The diameter of circle RST is 24 m and the perpendicular distance from R to the line ST is 18 m. as shown in Diagram below.
Find the perimeter of the platform.


Solution:

Given diameter = 24 m
hence radius = 12 m
O is the centre of the circle.
Using Pythagoras’ theorem:
x 2 = 12 2 6 2 x= 14436   =10.39 m TS=RS=RT  =10.39 m ×2  =20.78 m Perimeter of the platform TS+RS+RT =20.78×3 =63.34 m

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